In cosmology, the analysis of observational evidence is very important when testing theoretical models of the Universe. Artificial neural networks are powerful and versatile computational tools for data modelling and have recently been considered in the analysis of cosmological data. The main goal of this paper is to provide an introduction to artificial neural networks and to describe some of their applications to cosmology. We present an overview on the fundamentals of neural networks and their technical details. Through three examples, we show their capabilities in the modelling of cosmological data, numerical tasks (saving computational time), and the classification of stellar objects. Artificial neural networks offer interesting qualities that make them viable alternatives for data analysis in cosmological research.